I have this question (it's not a coursework question, I'm learning it by my own):(adsbygoogle = window.adsbygoogle || []).push({});

Use an appropiate power series expansion to find an asymptotic approximation as [tex]\epsilon[/tex] approaches 0+, correct to O(epsilon^2), for the two small roots of the equation: [tex]\epsilon x^3+x^2+2x-3=0[/tex] Then by using a suitable rescaling, find the first three terms of an asymptotic expansion as epsilon approaches 0+ of the singular root.

My way to go around this is to write down the next expansion series (because of the degree of the equation):

[tex]x(\epsilon)=\frac{1}{\epsilon^3}x_{-3}+ \frac{1}{\epsilon^2}x_{-2}+ \frac{1}{\epsilon^1}x_{-1}+x_0+x1\epsilon+...[/tex], the singular root is when epsilon equals null, i.e to solve x^2+2x-3=0=(x+3)(x-1) the roots are: x=-3 and x=1, I guess I need to choose the second root, now the recursive equation is:

[tex]x^2_{n+1}=-x_{n}/\epsilon-2/\epsilon+3/(x_{n}\epsilon)[/tex] Now, x0=1 and then use the iterative equation in order to find x_-3 and x_-2, am I correct or totally way off here?

Thanks in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Asymptotic Analysis question.

**Physics Forums | Science Articles, Homework Help, Discussion**